8 x² + 14 x + 5 = 0
2 ( 4 x² + 7 x ) = - 5
2 ( 4 x² + 7 x + 49/16 - 49/16 ) = -5
2 ( 4 x² + 7 x + 49/16 ) - 98/16 = - 5
2 ( 2 x + 7/4 )² = - 5 + 98/16
2 ( 2 x + 7/4 )² = -80/16 + 98/16
2 ( 2 x + 7/4 )² = 18/16 = 9/8 / : 2
( 2 x + 7/4 )² = 9/16 / √
2 x + 7/4 = 3/4
2 x = 3/4 - 7/4 = -1
x = - 1
and 2 x + 7/4 = -3/4
2 x = -7/4 - 3/4 = - 10/4= -5/2
x = - 5 / 4
Answer:
the answer is D.
Step-by-step explanation:
distribute property requires you to multiply the number outside the parenthesis in everything in the parenthesis. hope this helps.
A. x intercepts are where the graph hits the x axis or where f(x)=0
0=2x^2-x-10
solve
hmm
we can use the ac method
multiply 2 and -10 to get -20
what 2 numbers muliply to get -20 and add to get -1 (the coefint of the x term)
-5 and 4
split the midd into that
0=2x^2+4x-5x-10
group
0=(2x^2+4x)+(-5x-10)
factor
0=2x(x+2)-5(x+2)
undistribute
0=(x+2)(2x-5)
set each to 0
0=x+2
0=-2
0=2x-5
5=2x
5/2=x
x intercepts are at x=-2 and 5/2 or the points (-2,0) and (5/2,0)
B. ok, so for f(x)=ax^2+bx+c
if a>0, then the parabola opens up and the vertex is a minimum
if a<0 then the parabola opens down and the vertex is a max
f(x)=2x^2-x-10
2>0
opoens up
vertex is minimum
ok, the vertex
the x value of the vertex in f(x)=ax^2+bx+c= is -b/(2a)
the y value of the vertex is f(-b/(2a)) so
given
f(x)=2x^2-x-10
a=2
b=-1
-b/2a=-(-1)/(2*2)=1/4
f(1/4)=2(1/4)^2-(1/4)-10
f(1/4)=2(1/16)-1/4-10
f(1/4)=1/8-1/4-10
f(1/4)=1/8-2/8-80/8
f(1/4)=-81/8
so the vertex is (1/4,-81/8) or (0.25,-10.125)
C. graph the x intercepts and the vertex
the vertex is min and the graph goes through the x intercepts
Answer:
unrelated
Step-by-step explanation:
angle 1 and angle 6 are same-side, exterior angles, which is not in the options
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